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25 September 2022
 
  » arxiv » 1803.3246

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Dual loop quantizations of 3d gravity
Clement Delcamp ; Laurent Freidel ; Florian Girelli ;
Date 8 Mar 2018
AbstractThe loop quantization of 3d gravity consists in defining the Hilbert space of states satisfying the Gau{ss} constraint and the flatness constraint. The Gau{ss} constraint is enforced at the kinematical level by introducing spin networks which form a basis for the Hilbert space of gauge invariant functionals. The flatness constraint is implemented at the dynamical level via the Ponzano-Regge state-sum model. We propose in this work a dual loop quantization scheme where the role of the constraints is exchanged. The flatness constraint is imposed first via the introduction of a new basis labeled by group variables, while the Gau{ss} constraint is implemented dynamically using a projector which is related to the Dijkgraaf-Witten model. We discuss how this alternative quantization program is related to 3d teleparallel gravity.
Source arXiv, 1803.3246
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